This clinical trial hypothesizes that the use of novel combinations of antiretroviral therapy will lower HIV viral load among children with advanced or progressive HIV infection, and will be well-tolerated, similar to what has been observed among HIV-infected adults. The primary objectives of the study are to evaluate the following: 1) the reduction of HIV RNA among patients in each group when all antiretroviral agents are changed and at least 2 of the agents are novel, 2) the duration of the reduction in HIV RNA, 3) the safety and tolerance of these combinations based on clinical and laboratory toxicities, and 4) the steady-state pharmacokinetics of nevirapine, nelfinavir, and ritonavir when used in combination with respect to age and treatment group. Additional secondary objectives include evaluation of the clinical effects of combination therapy, the association of clinical and CNS measures with virologic indices, the presence of immunologic markers associated with immune reconstitution and the correlation of changes in HIV RNA with viral characteristics. This study is a Phase I/II, open-label, management algorithm for highly antiretroviral experienced HIV-infected children and adolescents with rapidly progressive or advanced HIV disease for whom current antiretroviral therapy is failing. It evaluates novel combinations of RTIs and PIs in reducing viral load, and evaluates the safety and pharmacokinetics of these combinations. Where novel agents in a particular class cannot be chosen because of extensive antiretroviral experience, a change from current therapy with administration of formerly experienced therapy is required.